Chapter 54
Presentation of
statistical data
54.1 Some statistical terminology
Data are obtained largely by two methods:
(a) by counting—for example, the number of stamps
sold by a post office in equal periods of time, and
(b) by measurement—for example, the heights of a
group of people.
When data are obtained by counting and only whole
numbers are possible, the data are called discrete. Measured data can have any value within certain limits and
are called continuous (see Problem 1).
A set is a group of data and an individual value within
the set is called a member of the set. Thus, if the masses
of five people are measured correct to the nearest 0.1 kg
and are found to be 53.1 kg, 59.4 kg, 62.1 kg, 77.8 kg and
64.4 kg, then the set of masses in kilograms for these five
people is:
{53.1, 59.4, 62.1, 77.8, 64.4}
and one of the members of the set is 59.4
A set containing all the members is called a population.
Some members selected at random from a population
are called a sample. Thus all car registration numbers
form a population, but the registration numbers of, say,
20 cars taken at random throughout the country are a
sample drawn from that population.
The number of times that the value of a member occurs
in a set is called the frequency of that member. Thus
in the set: {2, 3, 4, 5, 4, 2, 4, 7, 9}, member 4 has a frequency of three, member 2 has a frequency of two and
the other members have a frequency of one.
The relative frequency with which any member of a
set occurs is given by the ratio:
frequency of member
total frequency of all members
For the set: {2, 3, 5, 4, 7, 5, 6, 2, 8}, the relative frequency of member 5 is
2
9
Often, relative frequency is expressed as a percentage and the percentage relative frequency is: (relative
frequency × 100)%.
Problem 1. Data are obtained on the topics given
below. State whether they are discrete or continuous
data.
(a) The number of days on which rain falls in a
month for each month of the year.
(b) The mileage travelled by each of a number of
salesmen.
(c) The time that each of a batch of similar
batteries lasts.
(d) The amount of money spent by each of
several families on food.
(a) The number of days on which rain falls in a given
month must be an integer value and is obtained by
counting the number of days. Hence, these data
are discrete.
(b) A salesman can travel any number of miles (and
parts of a mile) between certain limits and these
data are measured. Hence the data are continuous.
Presentation of
statistical data
54.1 Some statistical terminology
Data are obtained largely by two methods:
(a) by counting—for example, the number of stamps
sold by a post office in equal periods of time, and
(b) by measurement—for example, the heights of a
group of people.
When data are obtained by counting and only whole
numbers are possible, the data are called discrete. Measured data can have any value within certain limits and
are called continuous (see Problem 1).
A set is a group of data and an individual value within
the set is called a member of the set. Thus, if the masses
of five people are measured correct to the nearest 0.1 kg
and are found to be 53.1 kg, 59.4 kg, 62.1 kg, 77.8 kg and
64.4 kg, then the set of masses in kilograms for these five
people is:
{53.1, 59.4, 62.1, 77.8, 64.4}
and one of the members of the set is 59.4
A set containing all the members is called a population.
Some members selected at random from a population
are called a sample. Thus all car registration numbers
form a population, but the registration numbers of, say,
20 cars taken at random throughout the country are a
sample drawn from that population.
The number of times that the value of a member occurs
in a set is called the frequency of that member. Thus
in the set: {2, 3, 4, 5, 4, 2, 4, 7, 9}, member 4 has a frequency of three, member 2 has a frequency of two and
the other members have a frequency of one.
The relative frequency with which any member of a
set occurs is given by the ratio:
frequency of member
total frequency of all members
For the set: {2, 3, 5, 4, 7, 5, 6, 2, 8}, the relative frequency of member 5 is
2
9
Often, relative frequency is expressed as a percentage and the percentage relative frequency is: (relative
frequency × 100)%.
Problem 1. Data are obtained on the topics given
below. State whether they are discrete or continuous
data.
(a) The number of days on which rain falls in a
month for each month of the year.
(b) The mileage travelled by each of a number of
salesmen.
(c) The time that each of a batch of similar
batteries lasts.
(d) The amount of money spent by each of
several families on food.
(a) The number of days on which rain falls in a given
month must be an integer value and is obtained by
counting the number of days. Hence, these data
are discrete.
(b) A salesman can travel any number of miles (and
parts of a mile) between certain limits and these
data are measured. Hence the data are continuous.